Xparts and Yparts Blender 2.63 or 2.72
This change was made in version 2.65, described in the release notes here under 'User Interaction'. You now have to define the size of the tiles by pixels in the performance panel, instead of defining how many tiles. For example, setting a tile to be 100px x 100px when rendering a 1000px x 1000px image would results in 10 tiles by 10 tiles.

However, I personally like to also have the option to define by the number of tiles, using the old way as you describe. I wrote a small addon which restores this functionality which can be found on github here, which adds back render parts options at the bottom of the performance panel: